TSTP Solution File: SWC246+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC246+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:21:04 EDT 2023
% Result : Theorem 27.72s 27.95s
% Output : CNFRefutation 27.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 105
% Syntax : Number of formulae : 234 ( 38 unt; 78 typ; 0 def)
% Number of atoms : 598 ( 176 equ)
% Maximal formula atoms : 48 ( 3 avg)
% Number of connectives : 742 ( 300 ~; 312 |; 60 &)
% ( 4 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 69 >; 19 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 59 ( 59 usr; 9 con; 0-3 aty)
% Number of variables : 256 ( 0 sgn; 122 !; 22 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ssItem: $i > $o ).
tff(decl_23,type,
neq: ( $i * $i ) > $o ).
tff(decl_24,type,
ssList: $i > $o ).
tff(decl_25,type,
memberP: ( $i * $i ) > $o ).
tff(decl_26,type,
cons: ( $i * $i ) > $i ).
tff(decl_27,type,
app: ( $i * $i ) > $i ).
tff(decl_28,type,
singletonP: $i > $o ).
tff(decl_29,type,
nil: $i ).
tff(decl_30,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_31,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_32,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_33,type,
cyclefreeP: $i > $o ).
tff(decl_34,type,
leq: ( $i * $i ) > $o ).
tff(decl_35,type,
totalorderP: $i > $o ).
tff(decl_36,type,
strictorderP: $i > $o ).
tff(decl_37,type,
lt: ( $i * $i ) > $o ).
tff(decl_38,type,
totalorderedP: $i > $o ).
tff(decl_39,type,
strictorderedP: $i > $o ).
tff(decl_40,type,
duplicatefreeP: $i > $o ).
tff(decl_41,type,
equalelemsP: $i > $o ).
tff(decl_42,type,
hd: $i > $i ).
tff(decl_43,type,
tl: $i > $i ).
tff(decl_44,type,
geq: ( $i * $i ) > $o ).
tff(decl_45,type,
gt: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_0: $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_1: $i > $i ).
tff(decl_51,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_1: $i > $i ).
tff(decl_58,type,
esk13_1: $i > $i ).
tff(decl_59,type,
esk14_1: $i > $i ).
tff(decl_60,type,
esk15_1: $i > $i ).
tff(decl_61,type,
esk16_1: $i > $i ).
tff(decl_62,type,
esk17_1: $i > $i ).
tff(decl_63,type,
esk18_1: $i > $i ).
tff(decl_64,type,
esk19_1: $i > $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_1: $i > $i ).
tff(decl_67,type,
esk22_1: $i > $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_1: $i > $i ).
tff(decl_71,type,
esk26_1: $i > $i ).
tff(decl_72,type,
esk27_1: $i > $i ).
tff(decl_73,type,
esk28_1: $i > $i ).
tff(decl_74,type,
esk29_1: $i > $i ).
tff(decl_75,type,
esk30_1: $i > $i ).
tff(decl_76,type,
esk31_1: $i > $i ).
tff(decl_77,type,
esk32_1: $i > $i ).
tff(decl_78,type,
esk33_1: $i > $i ).
tff(decl_79,type,
esk34_1: $i > $i ).
tff(decl_80,type,
esk35_1: $i > $i ).
tff(decl_81,type,
esk36_1: $i > $i ).
tff(decl_82,type,
esk37_1: $i > $i ).
tff(decl_83,type,
esk38_1: $i > $i ).
tff(decl_84,type,
esk39_1: $i > $i ).
tff(decl_85,type,
esk40_1: $i > $i ).
tff(decl_86,type,
esk41_1: $i > $i ).
tff(decl_87,type,
esk42_1: $i > $i ).
tff(decl_88,type,
esk43_1: $i > $i ).
tff(decl_89,type,
esk44_1: $i > $i ).
tff(decl_90,type,
esk45_1: $i > $i ).
tff(decl_91,type,
esk46_1: $i > $i ).
tff(decl_92,type,
esk47_1: $i > $i ).
tff(decl_93,type,
esk48_0: $i ).
tff(decl_94,type,
esk49_0: $i ).
tff(decl_95,type,
esk50_0: $i ).
tff(decl_96,type,
esk51_0: $i ).
tff(decl_97,type,
esk52_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk53_0: $i ).
tff(decl_99,type,
esk54_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) )
| ! [X9] :
( ssList(X9)
=> ! [X10] :
( ~ ssList(X10)
| app(app(X9,X3),X10) != X4
| ~ equalelemsP(X3)
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(X12,cons(X11,nil)) = X9
& ? [X13] :
( ssList(X13)
& app(cons(X11,nil),X13) = X3 ) ) )
| ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(cons(X14,nil),X15) = X10
& ? [X16] :
( ssList(X16)
& app(X16,cons(X14,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax51) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) )
| ! [X9] :
( ssList(X9)
=> ! [X10] :
( ~ ssList(X10)
| app(app(X9,X3),X10) != X4
| ~ equalelemsP(X3)
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(X12,cons(X11,nil)) = X9
& ? [X13] :
( ssList(X13)
& app(cons(X11,nil),X13) = X3 ) ) )
| ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& app(cons(X14,nil),X15) = X10
& ? [X16] :
( ssList(X16)
& app(X16,cons(X14,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_28,negated_conjecture,
! [X265,X266,X267,X271,X272,X273,X274,X275,X276] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssItem(esk52_3(X265,X266,X267))
| ~ ssList(X267)
| app(app(X266,cons(X265,nil)),X267) != esk48_0
| ~ ssList(X266)
| ~ ssItem(X265) )
& ( memberP(X266,esk52_3(X265,X266,X267))
| ~ ssList(X267)
| app(app(X266,cons(X265,nil)),X267) != esk48_0
| ~ ssList(X266)
| ~ ssItem(X265) )
& ( memberP(X267,esk52_3(X265,X266,X267))
| ~ ssList(X267)
| app(app(X266,cons(X265,nil)),X267) != esk48_0
| ~ ssList(X266)
| ~ ssItem(X265) )
& ( lt(X265,esk52_3(X265,X266,X267))
| ~ ssList(X267)
| app(app(X266,cons(X265,nil)),X267) != esk48_0
| ~ ssList(X266)
| ~ ssItem(X265) )
& ( ~ leq(X265,esk52_3(X265,X266,X267))
| ~ ssList(X267)
| app(app(X266,cons(X265,nil)),X267) != esk48_0
| ~ ssList(X266)
| ~ ssItem(X265) )
& ssList(esk53_0)
& ssList(esk54_0)
& app(app(esk53_0,esk50_0),esk54_0) = esk51_0
& equalelemsP(esk50_0)
& ( ~ ssItem(X271)
| ~ ssList(X272)
| app(X272,cons(X271,nil)) != esk53_0
| ~ ssList(X273)
| app(cons(X271,nil),X273) != esk50_0 )
& ( ~ ssItem(X274)
| ~ ssList(X275)
| app(cons(X274,nil),X275) != esk54_0
| ~ ssList(X276)
| app(X276,cons(X274,nil)) != esk50_0 )
& ( nil = esk51_0
| nil != esk50_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])]) ).
fof(c_0_29,plain,
! [X174,X175,X176] :
( ~ ssList(X174)
| ~ ssList(X175)
| ~ ssList(X176)
| ~ frontsegP(X174,X175)
| frontsegP(app(X174,X176),X175) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_30,plain,
! [X173] :
( ~ ssList(X173)
| frontsegP(X173,X173) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
cnf(c_0_31,negated_conjecture,
app(app(esk53_0,esk50_0),esk54_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X232,X233,X234] :
( ~ ssList(X232)
| ~ ssList(X233)
| ~ ssList(X234)
| app(app(X232,X233),X234) = app(X232,app(X233,X234)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_34,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
app(app(esk53_0,esk48_0),esk54_0) = esk51_0,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
app(esk53_0,app(esk48_0,esk54_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]),c_0_40])]) ).
fof(c_0_43,plain,
! [X140,X141] :
( ~ ssList(X140)
| ~ ssList(X141)
| ssList(app(X140,X141)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_44,plain,
! [X30,X31,X33] :
( ( ssList(esk6_2(X30,X31))
| ~ frontsegP(X30,X31)
| ~ ssList(X31)
| ~ ssList(X30) )
& ( app(X31,esk6_2(X30,X31)) = X30
| ~ frontsegP(X30,X31)
| ~ ssList(X31)
| ~ ssList(X30) )
& ( ~ ssList(X33)
| app(X31,X33) != X30
| frontsegP(X30,X31)
| ~ ssList(X31)
| ~ ssList(X30) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_45,negated_conjecture,
( frontsegP(esk51_0,esk53_0)
| ~ ssList(app(esk48_0,esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40])]) ).
cnf(c_0_46,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_48,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_49,plain,
! [X227,X228,X229] :
( ~ ssList(X227)
| ~ ssList(X228)
| ~ ssList(X229)
| app(X228,X229) != app(X228,X227)
| X229 = X227 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
cnf(c_0_50,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
frontsegP(esk51_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_38]),c_0_39])]) ).
cnf(c_0_52,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_54,plain,
! [X189,X190,X191] :
( ~ ssList(X189)
| ~ ssList(X190)
| ~ ssList(X191)
| ~ rearsegP(X189,X190)
| rearsegP(app(X191,X189),X190) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_55,plain,
! [X192] :
( ~ ssList(X192)
| rearsegP(X192,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_56,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,negated_conjecture,
app(esk53_0,esk6_2(esk51_0,esk53_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_40])]) ).
cnf(c_0_58,negated_conjecture,
ssList(esk6_2(esk51_0,esk53_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_40]),c_0_52])]) ).
cnf(c_0_59,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_62,negated_conjecture,
( X1 = esk6_2(esk51_0,esk53_0)
| app(esk53_0,X1) != esk51_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_40])]) ).
fof(c_0_63,plain,
! [X34,X35,X37] :
( ( ssList(esk7_2(X34,X35))
| ~ rearsegP(X34,X35)
| ~ ssList(X35)
| ~ ssList(X34) )
& ( app(esk7_2(X34,X35),X35) = X34
| ~ rearsegP(X34,X35)
| ~ ssList(X35)
| ~ ssList(X34) )
& ( ~ ssList(X37)
| app(X37,X35) != X34
| rearsegP(X34,X35)
| ~ ssList(X35)
| ~ ssList(X34) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
cnf(c_0_64,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_65,negated_conjecture,
( esk6_2(esk51_0,esk53_0) = app(esk48_0,esk54_0)
| ~ ssList(app(esk48_0,esk54_0)) ),
inference(spm,[status(thm)],[c_0_62,c_0_42]) ).
fof(c_0_66,plain,
! [X145] :
( ~ ssList(X145)
| app(nil,X145) = X145 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_67,plain,
! [X237] :
( ~ ssList(X237)
| app(X237,nil) = X237 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_68,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_57]),c_0_40]),c_0_58])]) ).
cnf(c_0_70,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,negated_conjecture,
esk6_2(esk51_0,esk53_0) = app(esk48_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_46]),c_0_38]),c_0_39])]) ).
cnf(c_0_72,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,negated_conjecture,
app(esk7_2(esk51_0,nil),nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_61]),c_0_52])]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk7_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_69]),c_0_61]),c_0_52])]) ).
cnf(c_0_76,negated_conjecture,
ssList(app(esk48_0,esk54_0)),
inference(rw,[status(thm)],[c_0_58,c_0_71]) ).
cnf(c_0_77,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_72]),c_0_61])]) ).
cnf(c_0_78,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_37]),c_0_61])]),c_0_46]) ).
cnf(c_0_79,negated_conjecture,
esk7_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_80,negated_conjecture,
( app(esk53_0,app(app(esk48_0,esk54_0),X1)) = app(esk51_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_40])]),c_0_76])]) ).
cnf(c_0_81,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_61])]) ).
cnf(c_0_82,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(rw,[status(thm)],[c_0_74,c_0_79]) ).
fof(c_0_83,plain,
! [X224,X225,X226] :
( ~ ssList(X224)
| ~ ssList(X225)
| ~ ssList(X226)
| app(X226,X225) != app(X224,X225)
| X226 = X224 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
cnf(c_0_84,negated_conjecture,
( X1 = app(esk48_0,esk54_0)
| app(esk53_0,X1) != esk51_0
| ~ ssList(X1) ),
inference(rw,[status(thm)],[c_0_62,c_0_71]) ).
cnf(c_0_85,negated_conjecture,
app(esk53_0,app(nil,app(esk48_0,esk54_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_61]),c_0_76])]) ).
cnf(c_0_86,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( app(nil,app(esk48_0,esk54_0)) = app(esk48_0,esk54_0)
| ~ ssList(app(nil,app(esk48_0,esk54_0))) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,plain,
( X1 = app(X2,X3)
| app(X1,X4) != app(X2,app(X3,X4))
| ~ ssList(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_37]),c_0_46]) ).
cnf(c_0_89,negated_conjecture,
app(nil,app(esk48_0,esk54_0)) = app(esk48_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_46]),c_0_76]),c_0_61])]) ).
cnf(c_0_90,negated_conjecture,
( X1 = app(nil,esk48_0)
| app(X1,esk54_0) != app(esk48_0,esk54_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_38]),c_0_39]),c_0_61])]) ).
cnf(c_0_91,negated_conjecture,
app(nil,esk48_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_90]),c_0_39])]) ).
fof(c_0_92,plain,
! [X240,X241] :
( ~ ssList(X240)
| ~ ssList(X241)
| nil = X240
| tl(app(X240,X241)) = app(tl(X240),X241) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_93,plain,
! [X137] :
( ~ ssList(X137)
| nil = X137
| ssList(tl(X137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_94,plain,
! [X177,X178,X179,X180] :
( ( X177 = X178
| ~ frontsegP(cons(X177,X179),cons(X178,X180))
| ~ ssList(X180)
| ~ ssList(X179)
| ~ ssItem(X178)
| ~ ssItem(X177) )
& ( frontsegP(X179,X180)
| ~ frontsegP(cons(X177,X179),cons(X178,X180))
| ~ ssList(X180)
| ~ ssList(X179)
| ~ ssItem(X178)
| ~ ssItem(X177) )
& ( X177 != X178
| ~ frontsegP(X179,X180)
| frontsegP(cons(X177,X179),cons(X178,X180))
| ~ ssList(X180)
| ~ ssList(X179)
| ~ ssItem(X178)
| ~ ssItem(X177) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
fof(c_0_95,plain,
! [X223] :
( ~ ssList(X223)
| nil = X223
| cons(hd(X223),tl(X223)) = X223 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_96,plain,
! [X238,X239] :
( ~ ssList(X238)
| ~ ssList(X239)
| nil = X238
| hd(app(X238,X239)) = hd(X238) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
fof(c_0_97,plain,
! [X235,X236] :
( ( nil = X236
| nil != app(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( nil = X235
| nil != app(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( nil != X236
| nil != X235
| nil = app(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_98,negated_conjecture,
rearsegP(esk48_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_91]),c_0_61]),c_0_39])]) ).
cnf(c_0_99,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_60]),c_0_61])]) ).
cnf(c_0_100,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_60]),c_0_61])]) ).
cnf(c_0_101,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,plain,
( frontsegP(cons(X1,X3),cons(X2,X4))
| X1 != X2
| ~ frontsegP(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
fof(c_0_104,plain,
! [X181] :
( ~ ssList(X181)
| frontsegP(X181,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_105,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_107,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_108,negated_conjecture,
app(esk7_2(esk48_0,nil),nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_98]),c_0_61]),c_0_39])]) ).
cnf(c_0_109,plain,
( esk7_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_99]),c_0_100]) ).
cnf(c_0_110,plain,
( nil = X1
| ssList(tl(app(X1,X2)))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_101]),c_0_102]) ).
cnf(c_0_111,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_103]) ).
cnf(c_0_112,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_113,plain,
( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_46]),c_0_107]) ).
cnf(c_0_114,negated_conjecture,
app(esk48_0,nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_39])]) ).
cnf(c_0_115,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_116,plain,
( nil = X1
| ssList(tl(app(nil,X1)))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_81]),c_0_61])]) ).
fof(c_0_117,plain,
! [X142,X143,X144] :
( ~ ssList(X142)
| ~ ssList(X143)
| ~ ssItem(X144)
| cons(X144,app(X143,X142)) = app(cons(X144,X143),X142) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(c_0_118,plain,
! [X121,X122] :
( ~ ssList(X121)
| ~ ssItem(X122)
| ssList(cons(X122,X121)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_119,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
fof(c_0_120,plain,
! [X129] :
( ( ssList(esk44_1(X129))
| nil = X129
| ~ ssList(X129) )
& ( ssItem(esk45_1(X129))
| nil = X129
| ~ ssList(X129) )
& ( cons(esk45_1(X129),esk44_1(X129)) = X129
| nil = X129
| ~ ssList(X129) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_121,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_61])]) ).
cnf(c_0_122,negated_conjecture,
cons(hd(esk48_0),tl(esk48_0)) = esk48_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_61]),c_0_39])]),c_0_115]) ).
cnf(c_0_123,negated_conjecture,
ssList(tl(esk48_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_91]),c_0_39])]),c_0_115]) ).
fof(c_0_124,plain,
! [X134] :
( ~ ssList(X134)
| nil = X134
| ssItem(hd(X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_125,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_126,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_127,plain,
( app(nil,X1) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_119]),c_0_61])]) ).
cnf(c_0_128,plain,
( X1 = X2
| ~ frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_129,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_130,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_131,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_132,negated_conjecture,
( frontsegP(esk48_0,cons(hd(esk48_0),nil))
| ~ ssItem(hd(esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).
cnf(c_0_133,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_134,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_125]),c_0_126]) ).
cnf(c_0_135,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_127]),c_0_61])]) ).
cnf(c_0_136,plain,
( esk45_1(X1) = X2
| nil = X1
| ~ frontsegP(X1,cons(X2,X3))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]),c_0_131]) ).
cnf(c_0_137,negated_conjecture,
frontsegP(esk48_0,cons(hd(esk48_0),nil)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_39])]),c_0_115]) ).
cnf(c_0_138,negated_conjecture,
( memberP(X1,esk52_3(X2,X1,X3))
| ~ ssList(X3)
| app(app(X1,cons(X2,nil)),X3) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_139,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_61])]) ).
fof(c_0_140,plain,
! [X230,X231] :
( ~ ssList(X230)
| ~ ssItem(X231)
| cons(X231,X230) = app(cons(X231,nil),X230) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_141,negated_conjecture,
( esk45_1(esk48_0) = hd(esk48_0)
| ~ ssItem(hd(esk48_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_61]),c_0_39])]),c_0_115]) ).
cnf(c_0_142,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_143,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_144,negated_conjecture,
( memberP(nil,esk52_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_72]),c_0_61])]),c_0_139]) ).
cnf(c_0_145,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_146,negated_conjecture,
esk45_1(esk48_0) = hd(esk48_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_133]),c_0_39])]),c_0_115]) ).
cnf(c_0_147,negated_conjecture,
( ssItem(esk52_3(X1,nil,X2))
| app(cons(X1,nil),X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_72]),c_0_61])]),c_0_139]) ).
fof(c_0_148,plain,
! [X167] :
( ~ ssItem(X167)
| ~ memberP(nil,X167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])]) ).
cnf(c_0_149,negated_conjecture,
( memberP(nil,esk52_3(X1,nil,X2))
| cons(X1,X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,negated_conjecture,
ssItem(hd(esk48_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_146]),c_0_39])]),c_0_115]) ).
cnf(c_0_151,negated_conjecture,
( ssItem(esk52_3(X1,nil,X2))
| cons(X1,X2) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_147,c_0_145]) ).
cnf(c_0_152,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_153,negated_conjecture,
memberP(nil,esk52_3(hd(esk48_0),nil,tl(esk48_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_122]),c_0_123]),c_0_150])]) ).
cnf(c_0_154,negated_conjecture,
ssItem(esk52_3(hd(esk48_0),nil,tl(esk48_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_122]),c_0_123]),c_0_150])]) ).
cnf(c_0_155,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC246+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 16:04:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 27.72/27.95 % Version : CSE_E---1.5
% 27.72/27.95 % Problem : theBenchmark.p
% 27.72/27.95 % Proof found
% 27.72/27.95 % SZS status Theorem for theBenchmark.p
% 27.72/27.95 % SZS output start Proof
% See solution above
% 27.72/27.96 % Total time : 27.387000 s
% 27.72/27.96 % SZS output end Proof
% 27.72/27.96 % Total time : 27.394000 s
%------------------------------------------------------------------------------